# How do you find the domain and range of y = 9 - x^2?

Mar 1, 2017

Domain: All real numbers. ($- \infty , \infty$)
Range:$\left(- \infty , 9\right]$

#### Explanation:

Lets use the graph of this function to help us here.

graph{9-x^2 [-20, 20, -10, 15]}

As you can see, this function is a parabola that opens down and has been shifted up 9 units.

Recall that domain is the interval of all possible x-values (independent variable) for the function. Since this is a polynomial function, the domain is all real numbers ($\mathbb{R}$)

Recall that the range of a function is all of the possible y-values (dependent variable) for this function. Looking at the graph, you can see that there are no y-values above 9. If we were to zoom out to infinity, we would also see that the graph goes down to $- \infty$. Therefore, the range would be $\left(- \infty , 9\right]$